Description: Closure of extended real multiplication. (Contributed by Mario Carneiro, 20-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | xmulcl | ⊢ ( ( 𝐴 ∈ ℝ* ∧ 𝐵 ∈ ℝ* ) → ( 𝐴 ·e 𝐵 ) ∈ ℝ* ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xmulf | ⊢ ·e : ( ℝ* × ℝ* ) ⟶ ℝ* | |
2 | 1 | fovcl | ⊢ ( ( 𝐴 ∈ ℝ* ∧ 𝐵 ∈ ℝ* ) → ( 𝐴 ·e 𝐵 ) ∈ ℝ* ) |